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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.am5c.01

 Input Form

 Hypergeometric2F1[3, 5, 23/4, z] == (1/(524288 (-1 + z)^2 z^(19/4))) (1045 (-8 z^(3/4) (1155 - 1804 z + 416 z^2 + 128 z^3) - (42 Sqrt[2] (165 - 352 z + 192 z^2) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(1/4) - (42 Sqrt[2] (165 - 352 z + 192 z^2) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(1/4) + (21 Sqrt[2] (165 - 352 z + 192 z^2) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(1/4) - (21 Sqrt[2] (165 - 352 z + 192 z^2) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(1/4)))

 Standard Form

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 MathML Form

 2 F 1 ( 3 , 5 ; 23 4 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["5", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["23", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] 1 524288 ( z - 1 ) 2 z 19 / 4 ( 1045 ( - 8 z 3 / 4 ( 128 z 3 + 416 z 2 - 1804 z + 1155 ) - 42 2 ( 192 z 2 - 352 z + 165 ) tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) 1 - z 4 - 42 2 ( 192 z 2 - 352 z + 165 ) tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) 1 - z 4 + 21 2 ( 192 z 2 - 352 z + 165 ) log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) 1 - z 4 - 21 2 ( 192 z 2 - 352 z + 165 ) log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) 1 - z 4 ) ) HypergeometricPFQ 3 5 23 4 z 1 524288 z -1 2 z 19 4 -1 1045 -8 z 3 4 128 z 3 416 z 2 -1 1804 z 1155 -1 42 2 1 2 192 z 2 -1 352 z 165 1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 1 -1 z 1 4 -1 -1 42 2 1 2 192 z 2 -1 352 z 165 z 1 4 2 1 2 1 -1 z 1 4 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 1 -1 z 1 4 -1 21 2 1 2 192 z 2 -1 352 z 165 z 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 1 -1 z 1 4 -1 -1 21 2 1 2 192 z 2 -1 352 z 165 z 1 2 1 -1 z 1 2 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 1 -1 z 1 4 -1 [/itex]

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2007-05-02